Space of modular forms of level 384 and weight 2

• Label: 384.2
• Level: 384
• Weight: 2
• Dimension: 1680
• Nonzero newspaces: 10
• Newform subspaces: 27
• Sturm bound: 16384
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 27 \)
Sturm bound:			\(16384\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(384))\).

	Total	New	Old
Modular forms	4416	1776	2640
Cusp forms	3777	1680	2097
Eisenstein series	639	96	543

Trace form

1680 * q - 12 * q^3 - 32 * q^4 - 16 * q^6 - 24 * q^7 - 20 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 8 * q^15 - 32 * q^16 - 16 * q^18 - 24 * q^19 - 4 * q^21 - 32 * q^22 + 16 * q^23 - 16 * q^24 - 8 * q^25 + 12 * q^27 - 32 * q^28 + 32 * q^29 - 16 * q^30 + 16 * q^31 - 32 * q^34 + 48 * q^35 - 16 * q^36 + 12 * q^39 - 32 * q^40 + 32 * q^41 - 16 * q^42 - 8 * q^43 + 4 * q^45 - 32 * q^46 - 16 * q^48 - 104 * q^49 - 96 * q^50 - 16 * q^51 - 224 * q^52 - 64 * q^53 - 48 * q^54 - 88 * q^55 - 224 * q^56 - 84 * q^57 - 320 * q^58 - 64 * q^59 - 208 * q^60 - 160 * q^61 - 192 * q^62 - 48 * q^63 - 416 * q^64 - 128 * q^65 - 208 * q^66 - 104 * q^67 - 192 * q^68 - 92 * q^69 - 416 * q^70 - 64 * q^71 - 16 * q^72 - 168 * q^73 - 224 * q^74 - 64 * q^75 - 288 * q^76 - 64 * q^77 - 112 * q^78 - 48 * q^79 - 96 * q^80 - 56 * q^81 - 32 * q^82 - 16 * q^84 - 112 * q^85 - 68 * q^87 - 32 * q^88 - 16 * q^90 - 24 * q^91 - 64 * q^93 - 32 * q^94 - 16 * q^96 - 64 * q^97 - 76 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
384.2.a	\(\chi_{384}(1, \cdot)\)	384.2.a.a	1	1
		384.2.a.b	1
		384.2.a.c	1
		384.2.a.d	1
		384.2.a.e	1
		384.2.a.f	1
		384.2.a.g	1
		384.2.a.h	1
384.2.c	\(\chi_{384}(383, \cdot)\)	384.2.c.a	4	1
		384.2.c.b	4
		384.2.c.c	4
		384.2.c.d	4
384.2.d	\(\chi_{384}(193, \cdot)\)	384.2.d.a	2	1
		384.2.d.b	2
		384.2.d.c	4
384.2.f	\(\chi_{384}(191, \cdot)\)	384.2.f.a	4	1
		384.2.f.b	4
		384.2.f.c	4
		384.2.f.d	4
384.2.j	\(\chi_{384}(97, \cdot)\)	384.2.j.a	8	2
		384.2.j.b	8
384.2.k	\(\chi_{384}(95, \cdot)\)	384.2.k.a	12	2
		384.2.k.b	12
384.2.n	\(\chi_{384}(49, \cdot)\)	384.2.n.a	32	4
384.2.o	\(\chi_{384}(47, \cdot)\)	384.2.o.a	56	4
384.2.r	\(\chi_{384}(25, \cdot)\)	None	0	8
384.2.s	\(\chi_{384}(23, \cdot)\)	None	0	8
384.2.v	\(\chi_{384}(13, \cdot)\)	384.2.v.a	512	16
384.2.w	\(\chi_{384}(11, \cdot)\)	384.2.w.a	992	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)